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In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

The order parameters and synchronization are numerically investigated in the time delay small-world connected FitzHugh–Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronization worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronization worsens also, and find that the larger rewiring probability becomes, the larger-order parameter. At the same time, the order parameter goes up, the time delay declines. We obtained the complete phase diagram for a wide range of values of noise intensity D and control parameter g. [ABSTRACT FROM AUTHOR]